Gravitational Constant G

τ-Formula

G = (c³/ℏ) · ι_τ² ≈ 6.674 × 10⁻¹¹

Derivation

The gravitational constant G is derived in Book V, Chapter 6 (High Energy and High Entropy at the Beginning), as part of the Opening Regime Theorem (V.T11). In the τ-framework, G is not a free parameter — it is read out from the D-sector coupling structure of the boundary holonomy algebra.

The τ-native expression for G follows from the identification of the D-sector (gravitational sector) coupling at depth 1: the gravitational coupling κ(D;1) = 1 − ι_τ = κ_D, combined with the dimensional calibration set by the neutron mass anchor (IV.D59). The gravitational constant emerges as G = (c³/ℏ) · ι_τ² in natural units, yielding G ≈ 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻² at approximately 3 ppm from the CODATA 2018 value.

The derivation depends on the Opening Regime Theorem (V.T11), which establishes that at the ignition depth the gravitational character is at its maximum — the boundary holonomy algebra first supports stable oscillating modes, and the gravitational coupling is structurally fixed by the sector template.

The closing identity α_G = α¹⁸ · √3 · (1 − 3α/π) (V.T20, the G–α Bridge) provides an independent cross-check: gravity and electromagnetism are connected by a single equation containing no free parameters.

Source

This prediction is derived in Book V, Part 1, Chapter 6 (High Energy and High Entropy at the Beginning), with the G–α Bridge identity in Book V, Part 8, Chapter 70.